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Consider the sequence of partial sums defined by s_n=sum_(k=1)^n(-1)^kk^(1/k). (1) As can be seen in the plot above, the sequence has two limit points at -0.812140... and ...

The (upper) matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree ...

The constant s_0 in Schnirelmann's theorem such that every integer >1 is a sum of at most s_0 primes. Of course, by Vinogradov's theorem, it is known that 4 primes suffice ...

A diagram lemma which states that the above commutative diagram of Abelian groups and group homomorphisms with exact rows gives rise to an exact sequence This commutative ...

For two polynomials P_1(x)=a_mx^m+...+a_0 and P_2=b_nx^n+...+b_0 of degrees m and n, respectively, the Sylvester matrix is an (m+n)×(m+n) matrix formed by filling the matrix ...

A well-covered graph is a graph for which every minimal vertex cover has the same size, which is equivalent to every maximal independent vertex set being the same size. It is ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...